The young midfielder entered the fray for Erik Lamela on 65 minutes and on 81 minutes, flung himself in at the far post to head us into the lead, his first Spurs goal.
But the Foxes hit back within a minute as dangerman Riyad Mahrez cut in from the right and hit an unstoppable shot into the far corner.
Both teams had late chances to win what was always an end-to-end encounter but in the end, both had to settle for share of the spoils in the Premier League.
Mauricio Pochettino made one change with Erik Lamela coming in for his first start of the season in place of injured Christian Eriksen (knee).
As expected, in-form Leicester, top of the table with two wins in two before kick-off, came flying out of the traps and enjoyed the early share of possession.
There were few clear-cut chances, however, and we had the first notable effort at goal on eight minutes when Mousa Dembele let fly from 20 yards, straight at Kasper Schmeichel.
We defended well in the first half with Toby Alderweireld blocking from Shinji Okazaki and then Ben Davies in the way of Mahrez's shot on 14 minutes. Marc Albrighton cut inside Dembele and Kyle Walker before firing wide on 18 minutes as the Foxes enjoyed their best spell.
We started to get a foothold in the game midway through the half and had the best chance of the opening period on 26 minutes when Eric Dier headed over Lamela's corner.
Schmeichel produced the best save of the half down to his left to turn away Dembele's low fizzer on the half-hour and the next clear-cut chance arrived in added time as Ryan Mason let fly from 20 yards only to find Wes Morgan in his way. Defences were definitely on top at the half drew to a close.
We started well in the second half and carved out an opening inside two minutes of the restart as Walker rolled in Chadli at the right angle of the box but the Belgian fired over.
Jan Vertonghen then burst down the left, beat Huth and crossed low for Lamela, who couldn't turn on target under pressure from Morgan.
Lamela's corners continued to cause Leicester problems and Chadli met two in quick succession only to guide his headers wide and over. In-between, Drinkwater hit low into the side-netting from 14 yards.
Chadli tried his luck again, this time drilling wide from 20 yards from Mason's pass before Kane weaved his way into the box from the left, beat three men and looked to pull the trigger on the stretch, only for Jeffrey Schlupp to get the slightest of touches to the effort and make it easy for Schmeichel.
Alli entered the fray midway through the half but it was Leicester on the offensive next as Drinkwater slid in Mahrez, right side and his low shot cannoned back off a combination of post and Hugo Lloris' foot.
Alli's moment arrived on 81 minutes. Kane released Chadli down the left and he lifted a delightful cross to the far post where Alli converted, diving in at the foot of the post.
Our joy lasted seconds though as just about from kick-off, Morgan launched long ball down our left, Drinkwater flicked on and Mahrez let fly from the right angle.
Lloris was perfectly positioned to block point-blank from Morgan with five minutes to go but we finished the stronger and Alli almost poked home the winner in injury time before the final chance, Alderweireld's shot from another corner blocked by Schlupp.
Leicester City (4-4-2): Schmeichel, De Laet, Huth, Morgan, Schlupp, Albrighton (Kante, 78), Drinkwater (Inler 80), King, Mahrez (Ulloa, 90+4), Okazaki, Vardy. Substitutes (not used): Schwarzer, Kramarić, Fuchs, Benalouane.
Spurs (4-2-3-1): Lloris (c), Walker, Alderweireld, Vertonghen, Davies, Dier, Mason (Bentaleb, 88), Dembele (Carroll 77), Chadli, Lamela (Alli 65), Kane. Substitutes (not used): Vorm, Rose, Trippier, Onomah.
Goals: Leicester - Mahrez (82); Spurs - Alli (81).
Yellow cards: Leicester - King (90+2); Spurs – Dembele (29), Lamela (31), Dier (60), Mason (84).
Referee: Martin Atkinson.